An inbox is the main folder that your incoming mail gets stored in. Whether you check your mail through a webmail interface or use a program like Outlook or Mac OS X Mail, each downloaded message gets stored in your inbox.
If you check your mail from a POP3 account using an e-mail program, the messages are downloaded to the inbox on your local hard drive. However, if you use an IMAP mail server, your inbox is created on the server and therefore your messages are stored on the server as well.
Because most people receive more mail than they can manage in one folder, it is common to create other folders to store your messages. After reading your messages, you may move them to other folders you have created (such as "Family," "Friends," "Business," etc.) or delete them by moving them to the Trash. However you decide to manage you mail, it is a good idea to keep the number of messages in your inbox from growing too large. Otherwise, you just might have to file for E-mail Bankruptcy.